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8.2 MULTIPLYING and FACTORING POLYNOMIALS:

Distributive Property: for any real numbers a, b, and c : a( b+c ) = ( b+c )a = ab + ac. 8.2 MULTIPLYING and FACTORING POLYNOMIALS:. Greatest Common Factor (GCF): The number, variable and/or term that each monomial or polynomial have in common . GOAL:. MULTIPLYING POLYNOMIALS:.

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8.2 MULTIPLYING and FACTORING POLYNOMIALS:

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  1. Distributive Property: for any real numbers a, b, and c : a(b+c) = (b+c)a = ab + ac. 8.2 MULTIPLYING and FACTORING POLYNOMIALS: Greatest Common Factor (GCF): The number, variable and/or term that each monomial or polynomial have in common.

  2. GOAL:

  3. MULTIPLYING POLYNOMIALS: When multiplying polynomials we must keep in mind the laws of exponents from chapter 7 and the distributive property. Ex: What is the simplest for of: –2x2 (7x3+5x2 – 12)

  4. MULTIPLYING POLYNOMIALS: Use the distributive property and exponent rules: –2x2(7x3+5x2 – 12) (–2)(7)x3x2+(–2)(5)x2x2– (–2)(12) x2 –14x5–10x4 + 24x2

  5. REAL-WORLD (x): We multiply polynomials using distributive property and exponential rules: Ex: A rectangular wooden frame has side lengths of 5x and 7x+1. The rectangular opening for a picture has side lengths of 3x and 5x. What is the area of the wooden part of the frame?

  6. SOLUTION: A rectangular wooden frame : 5x Area = b.h 7x+1 Area = (7x+1)(5x) Areaofoutside = 35x2 + 5x

  7. SOLUTION: The rectangular opening for a picture has side Area = b.h 3x Area = (5x)(3x) 5x Area = 15x2

  8. SOLUTION: What is the area of the wooden part of the frame? 3x 5x 5x 7x+1 Areaofoutside: 35x2 + 5x Areaofinside : - 15x2 Area of wood part:  20x2 + 5x

  9. FINDING THE GCF: Remember that the Greatest Common Factor (GCF) is what they have in common: Ex: What is the GCF of : 1) 5X3, 25x2 and 45x? 2) 9x6+15x4+12x2 3) p(p + 2) – 5(p + 2)

  10. FINDING THE GCF: Remember that the Greatest Common Factor (GCF) is what they have in common: 1) 5x3, 25x2 and 45x? In common: 5x3  5∙x∙x∙x 25x2  5∙5∙x∙x 5 x 45x  3∙3∙5∙x The GCF is 5x.

  11. FINDING THE GCF: Remember that the Greatest Common Factor (GCF) is what they have in common: 1) 9x6+15x4+12x2 9x6  3∙ 3∙x∙x∙x∙x∙x∙x In common: 15x4  3∙5∙x∙x∙x∙x 3xx = 3x2 12x2  3∙4∙x∙x The Factored form is: 3x2(3x4+5x2+4)

  12. FINDING THE GCF: Remember that the Greatest Common Factor (GCF) is what they have in common: 3) p(p + 2) – 5(p + 2) In common: p(p + 2)  p∙(p + 2) – 5(p + 2)  – 5∙(p + 2) (p + 2) The Factored form is: (p + 2)(p– 5)

  13. VIDEOS: Polynomials Multiplying Multiplying: https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/polynomial_tutorial/v/multiplying-polynomials

  14. VIDEOS: Greatest Common Factor https://www.khanacademy.org/math/algebra/polynomials/multiplying_polynomials/v/monomial-greatest-common-factor https://www.khanacademy.org/math/algebra/polynomials/multiplying_polynomials/v/factoring-and-the-distributive-property-2

  15. CLASSWORK:Page 477-478: Problems: As many as needed to master the concept

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